Tonal Pitch Space

Fred Lerdahl

Building on the foundation of Lerdahl and Jackendoff's influential A Generative Theory of Tonal Music, this volume presents a multidimensional model of diatonic and chromatic spaces that quantifies listeners' intuitions of the relative distances of pitches, chords, and keys from a given tonic.
The model is employed to assign prolongational structure, represent paths through the space, and compute patterns of tension and attraction as musical events unfold, thereby providing a partial basis for understanding musical narration, expectation, and expression. Conceived as both a
music-theoretic treatise and a contribution to the cognitive science of music, this book will be of interest to music theorists, musicologists, composers, computer musicians, and cognitive psychologists.

Reviews

"Tonal Pitch Space is one of the most important books to come along in music theory and music cognition in a while. The degree of detail that Lerdahl builds into his model is extraordinary, and the consistency with which he references not only the research literature of cognitive
psychology but also that of the full breadth of the history of music theory will ensure its importance to both groups of scholars for some time to come."--Computer Music Journal

"A Generative Theory of Tonal Music by Fred Lerdahl and Ray Jackendoff is one of the most important works in music
theory in the last half of the 20th century, and likewise it has taken its place among the foundational texts in music perception and cognition. Thus the publication of Lerdahl's Tonal Pitch Space, a book which extends the GTTM project, is a significant event."--Music Perception

"[Tonal PitchSpace] is an awe-inspiring achievement. It is bursting at the seams with interesting ideas and perceptive analytic insights. It breaks new ground in establishing rigorous, algorithmic procedures for sophisticated music theories and in forging strong connections between music theory and music
psychology. It engages other work in the field in the most exemplary way (one can only marvel at the wealth of references, not only to music theory past and present but also to psychology and other disciplines)--building on the ideas of others but always offering fresh insights and
perspectives."--Musicae Scientiae

"This book assembles and fully systematizes Lerdahl's work of the past decade and in many ways completes the project begun with 'A Generative Theory of Tonal Music.' In its scope, the detail of its argument, and in its claim to very precisely model musical
cognition on a grand scale, this work is virtually without precedent."--Christopher Hasty, Professor of Music, University of Pennsylvania

"Fred Lerdahl's 'Tonal Pitch Space' is an extraordinary achievement in music theory. It promises to have a major impact on our understanding of how music works
and how music is understood. It sketches a theory of enormous potential, with which theorists and cognitive scientists should be concerned for decades hence."--Jonathan Kramer, Professor of Music, Columbia University